Your two equations aren't linearly independent! Also you probably want to solve complex problem or you have 2 equations and 4 unknowns (re and im parts of b and c)
In[189]:= eq1a = (-0.6715589548470183` +
0.7409511253549592` I)/(0.7409511253549592` +
0.6715589548470183` I - b) + (-0.6715589548470183` +
0.7409511253549592` I)/(0.7409511253549592` +
0.6715589548470183` I - c)
Out[189]= -((0.671559 - 0.740951 I)/((0.740951 + 0.671559 I) - b)) - (
0.671559 - 0.740951 I)/((0.740951 + 0.671559 I) - c)
In[190]:= eq1b =
Simplify[%*((0.7409511253549592` + 0.6715589548470183` I) -
b)*((0.7409511253549592` + 0.6715589548470183` I) - c)]
Out[190]= (-1.99037 +
0.196034 I) + (0.671559 - 0.740951 I) b + (0.671559 - 0.740951 I) c
In[191]:= eq2a = (-0.20146768645410548` -
0.22228533760648775` I)/(0.22228533760648775` -
0.20146768645410548` I - b) + (-0.20146768645410548` -
0.22228533760648775` I)/(0.22228533760648775` -
0.20146768645410548` I - c)
Out[191]= -((0.201468 + 0.222285 I)/((0.222285 - 0.201468 I) - b)) - (
0.201468 + 0.222285 I)/((0.222285 - 0.201468 I) - c)
In[192]:= eq2b =
Simplify[%*((0.22228533760648775` - 0.20146768645410548` I) -
b)*((0.22228533760648775` - 0.20146768645410548` I) - c)]
Out[192]= (-0.179133 -
0.0176431 I) + (0.201468 + 0.222285 I) b + (0.201468 + 0.222285 I) c
In[193]:= eq1c =
Simplify[ComplexExpand[Im[eq1b], {b, c}]/0.7409511253549592`]
Out[193]= 0.264571 + 0.906347 Im[b] + 0.906347 Im[c] - 1. Re[b] -
1. Re[c]
In[194]:= eq2c =
Simplify[ComplexExpand[Im[eq2b], {b, c}]/0.22228533760648775`]
Out[194]= -0.0793713 + 0.906347 Im[b] + 0.906347 Im[c] + 1. Re[b] +
1. Re[c]
